Last Tuesday's attacks on the World Trade Centre and the Pentagon now appear to surpass the civil war battle of Antietam as the bloodiest day in American history. As Americans grieve for those who perished, they confront challenges that will test their common sense, their mettle, and their ideals.

The immediate challenge is to fashion a just and proper response. That first means determining who is responsible. All signs now point to Osama bin Laden. But it is not enough to identify likely culprits. Washington needs clear and credible evidence of responsibility. The international coalition the White House is assembling will fracture if it is asked to act based on hunches and surmises.

Only after the perpetrators are identified can we assess how best to respond. Would an attack on Afghanistan -even one that removes the Taliban from power - end its use as a terrorist haven? What if the investigation implicates not an international pariah like the Taliban but countries that are less isolated and better able to retaliate? Do we risk a wider war?

President Bush faces intense political pressure to act. Many Americans do not want to wait for investigations to unfold. Congress authorised Mr Bush to retaliate even before knowing whom he might retaliate against. Many dismiss concerns that innocent civilians might get caught in the crossfire.

But lashing out in a rage is no answer. No one benefits from the creation of a new generation of terrorists armed with fresh grievances. Nor does it honour the memory of those who perished last week to embrace the same disregard for innocent life as those responsible for their deaths.

There are signs the Bush administration understands this. Even as the White House put the US military on a war footing over the weekend, Mr Bush asked the American people for their "patience." He and his advisers recognise that the terrorist threat cannot be solved with a single military response or by military force alone. The US must make those responsible pay dearly - and it will. But it must do so in a way that serves American interests and fits American values.

Last week's attacks pose challenges to all Americans. Tolerance of people's differences is central to our civic religion even if we are not always faithful practitioners. Regrettably, that has been the case in recent days. Many Arab and Muslim Americans fear for their safety. Fortunately, episodes of violence have been isolated thus far. Many American politicians, including some such as the New York mayor, Rudy Giuliani, not known for being sensitive to ethnic minorities, have warned against anti-Arab and anti-Muslim bigotry.

Americans also face the challenge of adapting to a world in which terrorists can bring mass death to US soil. Will they toss away precious civil liberties in an anti-terrorist hysteria? Conversely, will they be willing to endure, for months and years to come, the inconveniences and sacrifices needed to foil terrorists?

Finally, Americans confront the challenge of deciding whether to remain engaged in the world. Some will argue that Tuesday's attacks prove that the world is a boiling cauldron of ethnic and national hatreds, and that we dabble in it at our peril. Such claims are not new. They dominated American thinking until Pearl Harbour. It would be an epic mistake, though, if Americans decided that safety lay in retreating into Fortress America. Isolationism is a not a real option. America's economy and interests are too deeply intertwined with the rest of the world to permit withdrawal.

The perpetrators of last week's tragedy were driven by hatred of the values that Americans, and by extension, all liberal societies, represent. That is why they targeted the twin towers of the World Trade Centre - powerful symbols of western capitalism and modernity. Changing what we do will not change who we are.

The temptation to turn inward can be resisted. For now Americans understand that international engagement is important. But proper political leadership, abroad as well as at home, is also essential. Nato's decision to invoke its mutual defence clause for the first time was critical, as will be what Nato does when reprisals do begin. If Washington is to remain engaged abroad, Americans need to know their allies will stand by them.

The US has known great challenges before. More often than not it has risen to meet them. With a little luck, and some calm and wise decision making, it will do so again.

James Lindsay is senior fellow at the Brookings Institution and former director of global issues on the White House National Security Council.